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Volume 12, Number 5, November 2001

The complete moment-curvature curves of doubly reinforced concrete beams made of normal-or
high-strength concrete have been evaluated using a newly developed analytical method that takes into
account the stress-path dependence of the constitutive properties of the materials. From the moment-curvature
curves and the strain distribution results obtained, the post-peak behavior and flexural ductility
of doubly reinforced normal- and high-strength concrete beam sections are studied. It is found that the
major factors affecting the flexural ductility of reinforced concrete beam sections are the tension steel
ratio, compression steel ratio and concrete grade. Generally, the flexural ductility decreases as the amount
of tension reinforcement increases, but increases as the amount of compression reinforcement increases.
However, the effect of the concrete grade on flexural ductility is fairly complicated, as will be explained
in the paper. Quantitative analysis of such effects has been carried out and a formula for direct evaluation
of the flexural ductility of doubly reinforced concrete sections developed. The formula should be useful
for the ductility design of doubly reinforced normal- and high-strength concrete beams.

Key Words
flexural ductility; high-strength concrete; moment-curvature behavior; reinforced concrete beams.

H.J. Pam, A.K.H. Kwan and J.C.M. Ho, Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

Remeshing strategies are formulated for r-adaptive and h/r-adaptive analysis of crack propaga-tion.
The relocation of the nodes, which typifies r-adaptivity, is a very cheap method to optimise a given
discretisation since the element connectivity remains unaltered. However, the applicability is limited. To
further improve the finite element mesh, a combined h/r-adaptive method is proposed in which h-adaptivity
is applied whenever r-adaptivity is not capable of further improving the discretisation. Two and
three-dimensional examples are presented. It is shown that the r-adaptive approach can optimise a
discretisation at minimal computational costs. Further, the combined h/r-adaptive approach improves the
performance of a fully r-adaptive technique while the number of h-remeshings is reduced compared to a
fully h-adaptive technique.

Key Words
adaptivity; remeshing; ALE; crack propagation; failure analysis; localisation.

H. Askes and L.J. Sluys, Faculty of Civil Engineering and Geosciences, Koiter Institute Delft, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
B.B.C. de Jong, TNO Building and Construction Research, P.O. Box 49, 2600 AA Delft, The Netherlands

In this paper, a new three-dimensional piezoelectric thin shell element containing an
integrated distributed piezoelectric sensor and actuator is proposed. The distributed piezoelectric sensor
layer monitors the structural shape deformation due to the direct effect and the distributed actuator layer
suppresses the deflection via the converse piezoelectric effect. A finite element formulation is presented
for static response of laminated shell with piezoelectric sensors/actuators. An eight-node and forty-DOF
shell element is built. The performance of the shell elements is improved by reduced integration
technique. The static shape control of structure is derived. The shell element is verified by calculating
piezoelectric polymeric PVDF bimorph beam. The results agreed with those obtained by theoretical
analysis, Tzou and Tseng (1990) and Hwang and Park (1993) fairly well. At last, the static shape control
of a paraboloidal antenna is presented.

Key Words
piezoelectric shell element; static shape control.

Su Huan Chen, Guo Feng Yao and Hua Dong Lian, Department of Mechanics, Jilin University, Nan-Ling Campus, Chang Chun, Jilin 130025, China

In standard finite element algorithms, the local stability conditions are not accounted for in
the formulation of the tangent stiffness matrix. As a result, the loss of the local stability is not adequately
related to the onset of the global instability. The phenomenon typically arises with material-type localizations,
such as shear bands and plastic hinges. This paper addresses the problem in the context of the planar,
finite-strain, rate-independent, materially non-linear beam theory, although the proposed technology is in
principle not limited to beam structures. A weak formulation of Reissner

Key Words
local stability; planar beam; finite element; numerical integration; plasticity.

Igor Planinc, Miran Saje and Bojan Cas, Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, SI-1115 Ljubljana, Slovenia

A new sort of learning algorithm named whole learning algorithm is proposed to simulate
the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A
mathematical technique to solve the multi-objective optimization problem is applied for the learning of the
feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error
vector defined as the difference between the outputs and the target values for all the learning data sets.
The change of the outputs is approximated in the first-order with respect to the amount of weight
modification of the network. The governing equation for weight modification to make the error vector
null is constituted with the consideration of the approximated outputs for all the learning data sets. The
solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of
the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients.
The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in
three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by
the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an

Key Words
neural network; whole learning algorithm; Moore-Penrose generalized inverse; material non-linearity; RC members; earthquake response.

Kayo Satoh, Nobuhiro Yoshikawa, Yoshiaki Nakano and Won-Jik Yang, Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

The design specifications of guard fences in Japan were reexamined and the revised
specifications were implemented from April 1999. Because of the huge consumption in time and cost to
test the performances of full-scale guard fences in the field, some assumptions are adopted while
modifying the design specifications, and numerical analyses are necessary to confirm the impact
performance and safety level of new types of steel highway guard fences. In this study, the finite element
models are developed for the heavy trucks and steel highway guard fences to reenact their behaviors, and
the solution approach is carried out using nonlinear dynamic analysis software of structures in three
dimensions (LS-DYNA). The numerical simulation results are compared with the full-scale on-site testing
results to verify the proposed analysis procedure. The collision process is simulated and it is also made
possible to visualize the movement of the truck and the performances of guard fences. In addition, the
energy shift of the truck kinetic energy to the truck and guard fence Internal energy, and the energy
absorption of each guard fence component are studied for the development of a new design methodology
of steel highway guard fences based on the energy absorption capacity.

Key Words
dynamic analysis; energy absorption; finite element method; guard fence; heavy truck; non-linear analysis; vehicle collision impact.

Yoshito Itoh and Chunlu Liu, Center for Integrated Research in Science and Engineering, Nagoya University, Nagoya 464-8603, Japan
Koichi Usami, Department of Civil Engineering, Nagoya University, Nagoya 464-8603, Japan

A numerical model, in the form of a computer program, for evaluating the fire resistance of
insulated wide-flange steel columns is presented. The three stages associated with the thermal and
structural analysis in the calculation of fire resistance of columns is explained. The use of the computer
program for tracing the response of an insulated steel column from the initial pre-loading stage to
collapse, due to fire, is demonstrated. The validity of the numerical model used in the program is
established by comparing the predictions from the computer program with results from full-scale fire tests.
Details of fire tests carried out on wide-flange steel columns protected with ceramic fibre insulation,
together with results, are presented. The computer program can be used to evaluate the fire resistance of
protected wide-flange steel columns for any value of the significant parameters, such as load, section
dimensions, column length, type of insulation, and thickness of insulation without the necessity of testing.

Key Words
fire resistance; computer program; high temperature; wide flange steel columns; insulated columns; contour protection.

V.K.R Kodur, Institute for Research in Construction, National Research Council, Ottawa, Canada
B.A. Ghani, Department of Mechanical Engineering, University Technology of Malaysia, Malaysia
M.A. Sultan and T.T. Lie, Institute for Research in Construction, National Research Council, Ottawa, Canada
M. El-Shayeb, Department of Mechanical Engineering, University Technology of Malaysia, Malaysia

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